Imagine you are thinking about a problem you need to solve, nothing's coming to mind, and all of a sudden you get a dozen different ideas at once. Is there a word that expresses this sudden flow of ideas? I could only find brainwave although I'm not sure if it refers to a flow of ideas rather than just one clever idea. I'm looking for a word that's commonly used.
"Brainwave(s)" is more commonly used in reference to an electrical impulse(s) in the brain, though Google does list its informal usage for a sudden clever idea.
For a more established and common term you could go with "flood," as in “a flood of ideas.” As to its frequency of usage, I found many Google hits, one of which I have linked, below.
Classic symptoms of hypomania include mild euphoria, a flood of ideas. See Wikipedia Hypomania
Ideation is the process of forming ideas. The Johnson O'Connor Research Foundation has a way of measuring the process of ideation. People to whom ideas come quickly and relatively effortlessly score high in ideation (I'm probably in the 95th percentile, according to their measurement). I'm assuming that the standard bell-shaped curve applies vis a vis ideation, with few people scoring very high or very low, and everyone one else falling somewhere within the curve.
I suggest, then, that a flood of ideation might suit your purposes. Perhaps a torrent of ideation would also suffice. Sometimes a paradigm shift instigates a flood of ideation, since along with a new way of looking at something (e.g., the universe, language, music, art), new ideas are bound to come flooding in, ideas which are compatible with the new--perhaps revolutionary--paradigm.